Can you test the CPU with a different cooler? Can you test the cooler on a different CPU?
A little gurgling at startup is common but (aside from very brief and very sporadic drippy or flushy sounds) it shouldn't really occur during normal operation. The inlet tube (from the rad to the block) would normally be cooler than the outlet tube (from the block to the rad) but it shouldn't be the sort of dramatic hot-vs-cold difference you describe.
Are any tubes pinched or blocked? If they're flexible then you can work your way pinch-wiggling them along their lengths until you find a clogged chunk or a blocked bubble or something. You can try "flexing" the rad a little to sense if there's shifting liquid/air mass within or scary creaking noises, you can do the same with the CPU block, shake it around and scrutinize carefully for cracks, etc. You can try tugging on all the connectors/fittings/etc. Basically inspect everything until you find a fault or you're confident there isn't a fault to be found.
I've never had an AIO leak but I've seen bad old AIOs which were pulled from machines at work, leaks are (extremely) rare but not impossible. In both cases there was no evidence of liquid residue/spills in the computers, only less liquid (and more air) inside the "closed" loops than expected ... so very slow "evaporation" leaks.
I have had an AIO pump shut down - a Kraken, lol - after almost 4 years of near-constant use. It started making bad noises, they gradually got louder, after a while it just seized up and BIOS alarm triggered system shutdown.
AIO blocks are the same as any other waterblock, they can get corroded or gunked up inside, although I've never opened one up for inspection.
If you're confident your TIM application was already done correctly then no point in another attempt. You could salvage some parts of a "faulty" AIO to build into a full DIY loop but it's probably better to just replace the AIO with another if you don't want the messy complications.
I'm always apprehensive about replacing hardware before identifying exactly which hardware is the fault which needs replacement, but we do what we gotta do, lol.
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